What is the Greatest Common Factor of 1730 and 1750?

Greatest common factor (GCF) of 1730 and 1750 is 10.

GCF(1730,1750) = 10

We will now calculate the prime factors of 1730 and 1750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1730 and 1750.

How to find the GCF of 1730 and 1750?

We will first find the prime factorization of 1730 and 1750. After we will calculate the factors of 1730 and 1750 and find the biggest common factor number .

Step-1: Prime Factorization of 1730

Prime factors of 1730 are 2, 5, 173. Prime factorization of 1730 in exponential form is:

1730 = 2¹ × 5¹ × 173¹

Step-2: Prime Factorization of 1750

Prime factors of 1750 are 2, 5, 7. Prime factorization of 1750 in exponential form is:

1750 = 2¹ × 5³ × 7¹

Step-3: Factors of 1730

List of positive integer factors of 1730 that divides 1730 without a remainder.

1, 2, 5, 10, 173, 346, 865

Step-4: Factors of 1750

List of positive integer factors of 1750 that divides 1730 without a remainder.

1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 125, 175, 250, 350, 875

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1730 and 1750. The biggest common factor number is the GCF number.
So the greatest common factor 1730 and 1750 is 10.

Also check out the Least Common Multiple of 1730 and 1750